I got an order validation too, but no download.
It also tried telling Origin wasn't installed, when it was clearly open on the right side of my screen. Fuuuuck you Origin
Im pretty sure they wait until a bunch of applications come through and then they are processed, not immediately after you register...
For me they said "Congratulations you're in!" and they gave me a download button. When I hit it, it said "Please install Origin". And now there's no option to download it anywhere.
EDIT: I guess this is a universal problem. I'll just wait.